Origin of vortex harmonic radiation from indium tin oxide thin films

Vortex harmonic radiation from an indium tin oxide thin film in the epsilon-near-zero (ENZ) regime, driven by an ultrashort ω₀ + 3ω₀ two-color field, is numerically investigated by solving the full-wave Maxwell equations with a nonlinear Kerr response. We show that the orbital angular momentum of the emitted harmonics provides a direct fingerprint of competing multiphoton pathways, because distinct photon-combination channels map onto harmonics with distinct topological charges and spatial profiles. For the fifth- and seventh-order harmonics, pathway competition is revealed through the evolution of intensity and spiral-phase structures with varying two-color amplitude ratios. Moreover, the ENZ regime is found to not only enhance harmonic generation but also preserve the topological stability of the emitted nonlinear modes.